aiqbench analysis
This paper proposes the Expected Utility Regret (EUR) rule, a novel framework for portfolio selection that achieves minimax and Bayes optimality without relying on specific prior distributions. By deriving mean-variance and risk-parity portfolios as special cases, it establishes new theoretical bounds for asymptotically optimal investment strategies based purely on data-driven regret minimization. While the mathematical finance context is central, the core contribution lies in advancing machine learning methods for decision-making under uncertainty, specifically within statistical learning theory.
Expected Utility Regret Rule: Minimax and Bayes Optimal Portfolio Choice
arXiv:2610.02290v1 Announce Type: cross Abstract: This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.
Abstract:This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.
Econometrics (econ.EM); Machine Learning (cs.LG); Statistics Theory (math.ST); Mathematical Finance (q-fin.MF); Machine Learning (stat.ML)
arXiv:2610.02290 [econ.EM]
(or arXiv:2610.02290v1 [econ.EM] for this version)
https://doi.org/10.48550/arXiv.2610.02290 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 287 words
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